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On the discrete kinetic theory for active particles. Mathematical tools

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
43
Identifiers
DOI: 10.1016/j.mcm.2005.10.001
Keywords
  • Kinetic Theory
  • Active Particles
  • Discrete Microscopic Variable
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract This paper deals with the development of a mathematical discrete kinetic theory to model the dynamics of large systems of interacting active particles whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity), but also peculiar functions, called activities, which are able to modify laws of classical mechanics. The number of the above particles is sufficiently large to describe the overall state of the system by a suitable probability distribution over the microscopic state, while the microscopic state is discrete. This paper deals with a methodological approach suitable to derive the mathematical tools and structures which can be properly used to model a variety of models in different fields of applied sciences. The last part of the paper outlines some research perspectives towards modelling.

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